Fig. 3: Multiple scattering and heralded electron spectra.

a, Time-averaged (not photon-correlated) electron spectrum (blue), modelled (red) by cascaded m-photon multiple-loss peaks (yellow) and an exponentially decaying continuum. b, Sketch of the electron-beam caustic traversing the waveguide with a convergence half-angle of α = 1.1 mrad, causing some spatial averaging of the coupling constant. c, Experimentally observed decay of the mean coupling strength towards larger impact parameters (distance from the waveguide). The s.d. is given as a grey background. The peak-height distributions at different \({g}_{0}^{{{\rm{EELS}}}}\) are included as insets. d, Energy distributions of uncorrelated (blue) and correlated electrons (red, yellow) for k detected photons (normalized to the area under the curves). The correlated spectra are obtained by summing over the background-subtracted coincidence peaks shown in Fig. 2c,d. e, Measured optical spectrum with a central peak width of about 80 nm, or 65 meV, normalized to the maximum value.